Discrete product systems of Hilbert bimodules
Discrete product systems of Hilbert bimodules
复制标题
希尔伯特双模离散积系统
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
N. Fowler
中科院分区：
文献类型：
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作者：
N. Fowler
Hilbert双模是C*-代数A上的右Hilbert模X，以及A的左作用作为X上的伴随算子。我们考虑希尔伯特双模族X = {X s：s E P}，由半群P索引，它被赋予一个乘法，实现同构X s <$A X t → X st ;这样的族称为乘积系统。定义了一个广义Cuntz-Pimsner代数Ox，证明了对于一个适当的乘积系统X，A与P的任意扭交叉积都可以实现为Ox.假设P是Nica意义下的拟格序，我们通过将O X的Toeplitz扩张T cov（X）嵌入到X扭曲的交叉积B P A T，X P中来分析O X的Toeplitz扩张T cov（X），我们的主要定理是B P X T，X P的忠实表示的一个特征.
A Hilbert bimodule is a right Hilbert module X over a C*-algebra A together with a left action of A as adjointable operators on X. We consider families X = {X s : s E P} of Hilbert bimodules, indexed by a semigroup P, which are endowed with a multiplication which implements isomorphisms X s ⊗ A X t → X st ; such a family is a called a product system. We define a generalized Cuntz-Pimsner algebra O x , and we show that every twisted crossed product of A by P can be realized as O x for a suitable product system X. Assuming P is quasi-lattice ordered in the sense of Nica, we analyze a certain Toeplitz extension T cov (X) of O X by embedding it in a crossed product B P A T,X P which has been twisted by X; our main Theorem is a characterization of the faithful representations of B P X T,X P.